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In 1964, the United Nations (UN) has launched a rocket flight to the Moon. A multi-national group of astronauts in the UN spacecraft land on the Moon, believing themselves to be the first lunar explorers. They discover a British Union Jack on the surface and a note naming Katherine Callender, claiming the Moon for Queen Victoria. Attempting to trace Callender, UN authorities find she has died, but find her husband Arnold Bedford now an old man in an old people's home. The nursing home staff do not let him watch television reports of the expedition because, according to the matron, it "excites him", dismissing his claims to have been on the Moon as insane delusion. The UN representatives question him about the Moon and he tells them his story. The rest of the film, as a flashback, shows what Bedford and Professor Cavor did in the 1890s.

In 1899, Arnold Bedford and his American fiancée Katherine Callender – known as Kate – meet an inventor, Joseph Cavor, who has invented Cavorite, a substance that will let anything it is applied to or made of deflect the force of gravity and which he plans to use to travel to the Moon. Cavor has already built a spherical spaceship for this purpose, taking Arnold and (accidentally) Kate with him. Whilst exploring the Moon, Bedford and Cavor fall down a vertical shaft and discover to their amazement an insectoid population, the Selenites, living beneath the surface. (Cavor coins this name for the creatures after the Greek goddess of the moon, Selene). After escaping from the Selenites back to the surface, they discover that their ship, still containing Kate (who stayed behind because Cavor had brought only two spacesuits), has been dragged into their underground city.

The two, following the drag trail, find and enter the city. The city holds a breathable atmosphere, so (unwisely) they remove and leave their spacesuit helmets. Upon finding the living quarters, they are attacked by a giant caterpillar-like "moon bull" which pursues them until the Selenites find out and are able to zap it to death with their electric-possessing stun ray gun. Cavor and Bedford see the city's power station, powered by sunlight. In the end they reach their ship underground. The Selenites quickly learn English and interrogate Cavor, who believes they wish to exchange scientific knowledge; this also leads up to Cavor having a speech with the "Grand Lunar", the lead Selenite. Bedford, however, realizes that the Selenites have no intention of letting them leave, and during a struggle with Cavor, accidentally fires a gun at the Grand Lunar. Running for their lives, Bedford manage to find the sphere and escape, but Cavor stays voluntarily on the Moon.

Bedford, along with Kate (who only leaves the ship once, to help repair the damage caused by the Selenites), flies the ship up a vertical shaft, shattering the window cover at the top, and back to Earth. The aged Bedford concludes his story by mentioning that the ship came down in the sea off Zanzibar, and sank, but he and Kate managed to swim ashore. There is no later radio message from Cavor, and his ultimate fate remains unknown.

Back in the present day, Bedford, the UN party and newspaper reporters watch on television the latest events on the Moon, where the US astronauts have broken into the Selenite city and find it deserted and decaying. Moments later, the ruined city starts to crumble and collapse, forcing the landing crew to retreat hastily, and seconds later the city is completely destroyed. Bedford realizes that the Selenites must have been killed off by Cavor's common coldviruses to which they had no immunity.

Cavor and Bedford have no radio and must make their helmets touch each other to talk in the vacuum (although the filmmakers violate this rule several times). It is not clear whether the Selenites have radio. The history of radio was only just starting when the 1890s events were set. Wireless communication from Cavor in the Moon appears in H. G. Wells's novel.